Gursoy, Buket, Mason, Oliver and Sergeev, Sergei (2013) The analytic hierarchy process, max algebra and multi-objective optimisation. Linear Algebra and its Applications, 438 (7). pp. 2911-2928. ISSN 0024-3795
Preview
OM_analytic hierarchy.pdf
Download (2MB) | Preview
Abstract
The analytic hierarchy process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche (2004, 2010) [10,11] introduced a max-algebraic approach to the single criterion AHP. We extend this to the multi-criteria AHP, by considering multi-objective generalisations of the single objective optimisation problem solved in these earlier papers. We relate the existence of globally optimal solutions to the commutativity properties of the associated matrices; we relate min–max optimal solutions to the generalised spectral radius; and we prove that Pareto optimal solutions are guaranteed to exist.
Item Type: | Article |
---|---|
Keywords: | Analytic hierarchy process (AHP); SR-matrix; Max algebra; Subeigenvector; Generalised spectral radius; Multi-objective optimization; |
Academic Unit: | Faculty of Science and Engineering > Research Institutes > Hamilton Institute |
Item ID: | 6066 |
Identification Number: | 10.1016/j.laa.2012.11.020 |
Depositing User: | Oliver Mason |
Date Deposited: | 23 Apr 2015 10:25 |
Journal or Publication Title: | Linear Algebra and its Applications |
Publisher: | Elsevier |
Refereed: | Yes |
Related URLs: | |
URI: | https://mu.eprints-hosting.org/id/eprint/6066 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
Repository Staff Only (login required)
Downloads
Downloads per month over past year